9y^2-6y-9=0

Solution for 9y^2-6y-9=0 equation:

Simplifying
9y2 + -6y + -9 = 0

Reorder the terms:
-9 + -6y + 9y2 = 0

Solving
-9 + -6y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -2y + 3y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -2y + 3y2)' equal to zero and attempt to solve:

Simplifying
-3 + -2y + 3y2 = 0

Solving
-3 + -2y + 3y2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-1 + -0.6666666667y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.6666666667y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.6666666667y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.6666666667y + y2 = 0 + 1
-0.6666666667y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.6666666667y + y2 = 1

The y term is -0.6666666667y.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667y + 0.1111111112 + y2 = 1 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667y + y2 = 1 + 0.1111111112

Combine like terms: 1 + 0.1111111112 = 1.1111111112
0.1111111112 + -0.6666666667y + y2 = 1.1111111112

Factor a perfect square on the left side:
(y + -0.3333333334)(y + -0.3333333334) = 1.1111111112

Calculate the square root of the right side: 1.054092553

Break this problem into two subproblems by setting 
(y + -0.3333333334) equal to 1.054092553 and -1.054092553.

Subproblem 1
y + -0.3333333334 = 1.054092553

Simplifying
y + -0.3333333334 = 1.054092553

Reorder the terms:
-0.3333333334 + y = 1.054092553

Solving
-0.3333333334 + y = 1.054092553

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + y = 1.054092553 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + y = 1.054092553 + 0.3333333334
y = 1.054092553 + 0.3333333334

Combine like terms: 1.054092553 + 0.3333333334 = 1.3874258864
y = 1.3874258864

Simplifying
y = 1.3874258864

Subproblem 2
y + -0.3333333334 = -1.054092553

Simplifying
y + -0.3333333334 = -1.054092553

Reorder the terms:
-0.3333333334 + y = -1.054092553

Solving
-0.3333333334 + y = -1.054092553

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + y = -1.054092553 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + y = -1.054092553 + 0.3333333334
y = -1.054092553 + 0.3333333334

Combine like terms: -1.054092553 + 0.3333333334 = -0.7207592196
y = -0.7207592196

Simplifying
y = -0.7207592196

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.3874258864, -0.7207592196}
Solution
y = {1.3874258864, -0.7207592196}